In this paper we investigate the single and double ionization signals of H2 molecules, with fixed and moving nuclei, as a function of laser intensity, for two different values of laser wavelength =390 nm and =780 nm, using an approach for evaluating the ionization signals which allows the investigation of rela- tively long-lasting pulses. The He system is first investigated to benchmark our calculation against already known results. We confirm the evidence of nonsequentiality in the ionization processes of all the systems investigated. Furthermore, we show that the nuclei motion enhances the double ionization signals by means of a mechanism which is very similar to a charge-resonant enhanced ionization CREI effect Zuo and Bandrauk, Phys. Rev. A 52, R2511 1995
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